A polynomial-time algorithm for learning nonparametric causal graphs
This work addresses the challenge of causal inference in complex, nonlinear systems for researchers in statistics and machine learning, representing a significant advancement beyond linear models.
The authors tackled the problem of learning nonlinear, nonparametric directed acyclic graphical (DAG) models from data without assumptions like linearity or faithfulness, and established finite-sample guarantees for a polynomial-time algorithm with an additional cost linear in dimension and sample size compared to an optimal oracle algorithm.
We establish finite-sample guarantees for a polynomial-time algorithm for learning a nonlinear, nonparametric directed acyclic graphical (DAG) model from data. The analysis is model-free and does not assume linearity, additivity, independent noise, or faithfulness. Instead, we impose a condition on the residual variances that is closely related to previous work on linear models with equal variances. Compared to an optimal algorithm with oracle knowledge of the variable ordering, the additional cost of the algorithm is linear in the dimension $d$ and the number of samples $n$. Finally, we compare the proposed algorithm to existing approaches in a simulation study.